Psalm 16 is a very problematic psalm, and for a gaggle of reasons:
1. Most scholars consider this to be a Song of Confidence or Trust like Psalm 23, yet it begins with a very lament-like plea for help in verse 1. Recent scholarship, helpfully, sees this "plea" as a devout desire for continuing protection in general rather than a specific request.
2. The intractable verses 3-4 are among the most untranslatable verses in the book of Psalms, if not in the entire Old Testament. Some translations, like the New Revised Standard Version and the Revised English Bible, take "holy ones in the land" and "nobles" as an orthodox community of saints towards whom the psalmist is positively disposed. Other translations, like the New American Bible, the New Jerusalem Bible, and the Jewish Publication Society's Tanak, take them as vile Canaanite deities that the psalmist rejects. It is impossible to decide which is correct. Regardless of ones decision in this matter, the psalmist is clearly opting for Yahweh over other gods.
3. Virtually everyone reads the first word of verse 2 as "I say" (some LXX witnesses, Syriac) despite its clear reading of "you have said" (amart) in the Masoretic Text. If the correct reading is "I say," verses 2-4 must be read as a powerful confession of trust. If the correct reading is "you have said," then verse 4 must be seen as the psalmist's coldblooded rebuke of the spineless waffling between someone's alleged trust in Yahweh in verse 2 and their pandering to other "gods" in verse 3. Again, there is no practical way to resolve this enigma.
4. Ever since Peter preached on this text at the first Pentecost (Acts 2), the church has read this psalm as a messianic prophecy of Christ's resurrection. More on this later!
5. The psalm's structure and progression of thought continue to baffle one and all with its obscurity. The following is tentatively offered as a barely possible structural presentation of the psalm that assumes:
A Confession of trust in Yahweh (1-2)
B Yahweh's holy ones favored (3)
B' Those who choose another god rejected (4)
A' Confession of trust in Yahweh (5-6)
This view of the structure sees the psalm as essentially a Confession of Confidence or Trust, at least through the first six verses. The parallels between AA' and BB' strengthen this perception. The last half of the psalm becomes an extended reflection on the psalmist's joy and security that comes from recognition of Yahweh as God, especially as that is seen in the divine instruction offered at every turn.
Recent attempts to understand this psalm have drawn attention to four terms in verses 5-6 associated with the distribution of the land among the tribes of Israel after the occupation of the land of Canaan, as recorded in the book of Joshua (chapters 13-17):
The Lord is my chosen portion and my cup;
you hold my lot.
The boundary lines have fallen for me in pleasant places;
I have a goodly heritage (Psalm 16:5-6)
This may mean the psalmist is trying to describe his joy at the goodness of his experience of life at the hand of the LORD in terms of God's gracious gift of the land long promised to Abraham. Just as God had distributed each portion of the land by lot with boundary lines indicating the heritage of the tribes, so the psalmist has received only goodness in his "pleasant places" from God.
But now the second half of the psalm comes into play. The psalmist is not waxing eloquent upon his possession of the promised land in a woodenly literal way; rather, it is the teaching, counsel, guidance, and revelation of the LORD (7-8, 11) that call forth his praise. These expressions of gratitude in turn frame the psalmist's declaration that his inner being ("my heart," "my soul," [kevodi sounds like kevedi "my liver" in Hebrew!], "me," [literally, "my throat"]) will "be glad" and "rejoice," while his external being ("my body") will "rest secure" and not experience the "corruption" (LXX) of "the Pit" (9-10).
Be that as it may, the obvious reason for the inclusion of Psalm 16 as a response to this week's First Reading from Daniel is found in verse 10 and its possible allusion to life beyond the grave. A similar promise is contained in Dan 12:2. Should the preacher "go there?" The psalmist, after all, has reinterpreted the traditional land/inheritance imagery of Joshua to sing of his own experience with God. Whether the preacher wants to "go there" in the sermon . . . (as Peter did!), try the psalmist's own spiritualized re-telling of the occupation of the promised land, or stay with the more contextual reading offered here is strictly a matter of personal choice.